Once again, I followed your links and didn't find any proposals for changing Social Security.
People with serious proposals, and enough political clout, can get them "scored" by the SS actuaries. Here's a link
Proposals addressing Social Security solvency
You'll see there are about 30 over an 8 year period. None of them were proposed by Bush. I think he doesn't want to get specific enough to get pinned down.
The "President's Commission" made 3 proposals. I don't have any source that says Bush publicly supported any one of them.
Here is some typical language on personal accounts, this happens to be from "Model 2".
The basic idea here is that the gov't borrows money so it can lend it to workers. They invest the money while they are working, then at retirement they repay the gov't with interest. If the gov't charges the same rate it pays, and the workers invest in gov't bonds, they gain exactly nothing. The suggestion that workers would be far ahead of traditional SS by adopting this proposal and investing in bonds is false.
If one worker took the loan and invested in stocks, that worker would (probably) come out ahead. However, if all the workers did that, they would force an increase in interest rates on all gov't debt. The workers gains would be offset by losses that all taxpayers would incur due to the extra interest. (It's a zero-sum game because there is no net saving.)
Maybe you have a different proposal in mind. I can't claim that I've looked at more than a couple of the others. If you want to show me which one doesn't involve additional taxes or borrowing, or lower benefits, I'd be willing to look at it with you.